Special topics

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Special topics
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Importance of a variable
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Death penalty example

• . sum death bd- yv
• Variable Obs Mean Std. Dev.
  Min Max
• -------------------------------------------------
  --------------------
• death 100 .49 .5024184
  0 1
• bd 100 .53 .5016136
  0 1
• wv 100 .74 .440844
  0 1
• ac 100 .4366667 .225705
  0 1
• fv 100 .31 .4648232
  0 1
• -------------------------------------------------
  --------------------
• vs 100 .51 .5024184
  0 1
• v2 100 .14 .3487351
  0 1
• ms 100 .12 .3265986
  0 1
• yv 100 .08 .2726599
  0 1

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Death penalty example

• . reg death bd-yv , beta
• ------------------------------------------------
• death Coef. Std. Err. Pgtt Beta
• ------------------------------------------------
• bd -.0869168 .1102374 0.432 -.0867775
• wv .3052246 .1207463 0.013 .2678175
• ac .4071931 .2228501 0.071 .1829263
• fv .0790273 .1061283 0.458 .0731138
• vs .3563889 .101464 0.001 .3563889
• v2 .0499414 .1394044 0.721 .0346649
• ms .2836468 .1517671 0.065 .1843855
• yv .050356 .1773002 0.777 .027328
• _cons -.1189227 .1782999 0.506 .
• -------------------------------------------------

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Importance of a variable

• Three potential answers
• Theoretical importance
• Level importance
• Dispersion importance

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Importance of a variable

• Theoretical importance
• Theoretical importance Regression coefficient
  (b)
• To compare explanatory variables, put them on
  the same scale
• E.g., vary between 0 and 1

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Importance of a variable

• Level importance most important in particular
  times and places
• E.g., did the economy or presidential popularity
  matter more in congressional races in 2006?
• Level importance bj xj

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Importance of a variable

• Dispersion importance what explains the variance
  on the dependent variable
• E.g., given that the GOP won in this particular
  election, why did some people vote for them and
  others against?
• Dispersion importance
• Standardized coefficients, or alternatively
• Regression coefficient times standard deviation
  of explanatory variable
• In bivariate case, correlation

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Which to use?

• Depends on the research question
• Usually theoretical importance
• Sometimes level importance
• Dispersion importance not usually relevant

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Interactions
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Interactions

• How would we test whether defendants are
  sentenced to death more frequently for killing
  white strangers then you would expect from the
  coefficients on white victim and on victim
  stranger?
• . tab wv vs
• vs
• wv 0 1 Total
• -------------------------------------------
• 0 12 14 26
• 1 37 37 74
• -------------------------------------------
• Total 49 51 100

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Interactions

• . g wvXvs wv vs
• . reg death bd yv ac fv v2 ms wv vs wvXvs
• -----------------------------------------------
• death Coef. Std. Err. t Pgtt
• ----------------------------------------------
• (omitted)
• wv .0985493 .1873771 0.53 0.600
• vs .1076086 .2004193 0.54 0.593
• wvXvs .3303334 .2299526 1.44 0.154
• _cons .0558568 .2150039 0.26 0.796
• -----------------------------------------------

• To interpret interactions, substitute the
  appropriate values for each variable
• E.g., whats the effect for
• .099wv.108vs
  .330wvXvs
• White, non-stranger .099(1).108(0).330(1)X(0)
  .099
• White, stranger .099(1).108(1).330(1)X(
  1) .537
• Black, non-stranger .099(0).108(0).330(0)X(0)
  comparison
• Black, stranger .099(0).108(1).330(1)X(
  0) .108

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Interactions

• . tab wv vs, sum(death)
• Means, Standard Deviations and Frequencies of
  death
• vs
• wv 0 1 Total
• -------------------------------------------
• 0 .16666667 .28571429 .23076923
• .38924947 .46880723 .42966892
• 12 14 26
• -------------------------------------------
• 1 .40540541 .75675676 .58108108
• .49774265 .43495884 .4967499
• 37 37 74
• -------------------------------------------
• Total .34693878 .62745098 .49
• .48092881 .48829435 .50241839
• 49 51 100

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Analyzing and presenting your data
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Analyzing and presenting your data

• Code your variables to vary between 0 and 1
• Use replace or recode commands
• Makes coefficients comparable
• To check your coding and for missing values,
  always run summary before running regress
• sum y x1 x2 x3
• reg y x1 x2 x3
• Always present the bivariate results first, then
  the multiple regression (or other) results
• Never present raw Stata output and papers

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Partial residual scatter plots
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Partial residual scatter plots

• Importance of plotting your data
• Importance of controls
• How do you plot your data after youve adjusted
  it for control variables?
• Example inferences about candidates in Mexico
  from faces

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Greatest competence disparity pairing 10

• Gubernatorial race
• A more competent
• Who won?
• A by 65

A
B
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Regression

• Source SS df MS
  Number of obs 33
• -------------------------------------------
  F( 3, 29) 4.16
• Model .082003892 3 .027334631
  Prob gt F 0.0144
• Residual .190333473 29 .006563223
  R-squared 0.3011
• -------------------------------------------
  Adj R-squared 0.2288
• Total .272337365 32 .008510543
  Root MSE .08101
• --------------------------------------------------
  ----------------------------
• vote_a Coef. Std. Err. t
  Pgtt 95 Conf. Interval
• -------------------------------------------------
  ----------------------------
• competent .1669117 .0863812 1.93
  0.063 -.0097577 .343581
• incumbent .0110896 .0310549 0.36
  0.724 -.0524248 .074604
• party_a .2116774 .1098925 1.93
  0.064 -.013078 .4364327
• _cons .2859541 .0635944 4.50
  0.000 .1558889 .4160194
• --------------------------------------------------
  ----------------------------
• vote_a is vote share for Candidate A
• incumbent is a dummy variable for whether the
  party currently holds the office
• party_a is the vote share for the party of
  Candidate A in the previous election

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Calculating partial residuals

• First run your regression with all the relevant
  variables
• . reg vote_a competent incumbent party_a
• To calculate the residual for the full model, use
• . predict e, res
• (This creates a new variable e, which equals to
  the residual.)
• Here, however, we want to generate the residual
  controlling only for some of the variables. To do
  this, we could manually predict vote_a based only
  on incumbent and party_a
• . g y_hat 0.167 incumbent.011 party_a.212
• We can then generate the partial residual
• . g partial_e vote_a y_hat
• Instead, can use the Stata adjust
• . adjust competent 0, by(incumbent party_a)
  gen(y_hat)
• . g partial_e vote_a y_hat

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Calculating partial residuals

• Regression of the partial residual on competent
  should give you the same coefficient as in the
  earlier regression. It does.
• . reg partial_e competent
• Source SS df MS
  Number of obs 33
• -------------------------------------------
  F( 1, 31) 4.52
• Model .027767147 1 .027767147
  Prob gt F 0.0415
• Residual .190333468 31 .006139789
  R-squared 0.1273
• -------------------------------------------
  Adj R-squared 0.0992
• Total .218100616 32 .006815644
  Root MSE .07836
• --------------------------------------------------
  ----------------------------
• e Coef. Std. Err. t
  Pgtt 95 Conf. Interval
• -------------------------------------------------
  ----------------------------
• competent .1669117 .078487 2.13
  0.042 .0068364 .326987
• _cons -7.25e-09 .0470166 -0.00
  1.000 -.0958909 .0958909
• --------------------------------------------------
  ----------------------------

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• Compare scatter plot (top) with residual scatter
  plot (bottom)
• Residual plots especially important if results
  change when adding controls

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Imputing missing data
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Imputing missing data

• Variables often have missing data
• Sources of missing data
• Missing data reduces estimate precision and may
  bias estimates
• To rescue data with missing cases impute using
  other variables
• Imputing data can
• Increase sample size and so increase precision of
  estimates
• Reduce bias if data is not missing at random

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Imputation example

• Car ownership in 1948
• Say that some percentage of sample forgot to
  answer a question about whether they own a car
• The data set contains variables that predict car
  ownership family_income, family_size, rural,
  urban, employed

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Stata imputation command

• impute depvar varlist weight if exp in
  range, generate(newvar1)
• depvar is the variable whose missing values are
  to be imputed.
• varlist is the list of variables on which the
  imputations are to be based
• newvar1 is the new variable to contain the
  imputations
• Example
• impute own_car family_income family_size rural
  suburban employed, g(i_own_car)

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Rules about imputing

• Before you estimate a regression model, use the
  summary command to check for missing data
• Before you impute, check that relevant variables
  actually predict the variable with missing values
  (use regression or other estimator)
• Dont use your studies dependent variable or key
  explanatory variable in the imputation
  (exceptions)
• Dont impute missing values on your studies
  dependent variable express (exceptions)
• Always note whether imputation changed results
• If too much data as missing, imputation wont help